Probabilistic Symmetries and Invariance Principles

Olav Kallenberg

ISBN 10: 1441920420 / ISBN 13: 9781441920423

Editore: Springer New York, Springer US Dez 2010, 2010

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Neuware -This book is about random objects¿sequences, processes, arrays, measures, functionals¿with interesting symmetry properties. Here symmetry should beunderstoodinthebroadsenseofinvarianceunderafamily(notnecessarily a group) of measurable transformations. To be precise, it is not the random objects themselves but rather their distributions that are assumed to be symmetric. Though many probabilistic symmetries are conceivable and have been considered in various contexts, four of them¿stationarity, contractability, exchangeability, and rotatability¿stand out as especially interesting and - portant in several ways: Their study leads to some deep structural theorems of great beauty and signi cance, they are intimately related to some basic areasofmodernprobabilitytheory, andtheyaremutuallyconnectedthrough a variety of basic relationships. The mentioned symmetries may be de ned as invariance in distribution under shifts, contractions, permutations, and rotations. Stationarity being a familiar classical topic, treated extensively in many standard textbooks and monographs, most of our attention will be focused on the remaining three basic symmetries. The study of general probabilistic symmetries essentially originated with the work of de Finetti (1929¿30), who proved by elementary means (no - vanced tools being yet available) the celebrated theorem named after him¿ the fact that every in nite sequence of exchangeable events is mixed i.i.d.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 524 pp. Englisch.

Codice articolo 9781441920423

Dati bibliografici

• Titolo: Probabilistic Symmetries and Invariance Principles
• Editore: Springer New York, Springer US Dez 2010
• Data di pubblicazione: 2010
• Lingua: Inglese
• ISBN 10: 1441920420
• ISBN 13: 9781441920423
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 235 L x 155 A x 29 P (millimetri) 235 millimetri di larghezza per 155 millimetri di altezza per 29 millimetri di profondità
• Peso: 785 grammi

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Riassunto

This book is about random objects--sequences, processes, arrays, measures, functionals--with interesting symmetry properties.

Informazioni sull?autore

Olav Kallenberg received his Ph.D. in 1972 from Chalmers University in Gothenburg, Sweden. After teaching for many years at Swedish universities, he moved in 1985 to the US, where he is currently Professor of Mathematics at Auburn University. He is well known for his previous books Random Measures (4th edition, 1986) and Foundations of Modern Probability (2nd edition, 2002) and for numerous research papers in all areas of probability. In 1977, he was the second recipient ever of the prestigious Rollo Davidson Prize from Cambridge University. In 1991–94, he served as the Editor in Chief of Probability Theory and Related Fields. Professor Kallenberg is an elected fellow of the Institute of Mathematical Statistics.